QUASI-SEMI-HOMOMORPHISMS AND GENERALIZED PROXIMITY RELATIONS BETWEEN BOOLEAN ALGEBRAS

SERGIO ARTURO CELANI

Miskolc Mathematical Notes

Miskolc University

Lugar: Miskolc; Año: 2018 vol. 19 p. 171 - 189

1787-2405

In this paper we shall introduce the notion of quasi-semi-homomorphismsbetween Boolean algebras, as a generalization of the quasi-modal operatorsintroduced in cite{Celani}, of the notion of meet-homomorphism studiedin cite{Halmos} and cite{Graf}, and the notion of precontact orproximity relation defined in cite{D=0000FCntsch-Vakarelov2007}.We will prove that the class of Boolean algebras with quasi-semi-homomorphismis a category, denoted by $mathbf{BoQS}$. We shall prove that thiscategory is equivalent to the category $mathbf{StQB}$ of Stone spaceswhere the morphisms are binary relations, called quasi-Boolean relations,satisfying additional conditions. This duality extends the dualityfor meet-homomorphism given by P. R. Halmos in cite{Halmos} andthe duality for quasi-modal operators proved in cite{Celani}.